The far-infrared–radio correlation (FRC) is one of the most promising empirical constraints on the role of cosmic rays (CRs) and magnetic fields in galaxy formation and evolution. While many theories have been proposed in order to explain the emergence and maintenance of the FRC across a gamut of galaxy properties and redshift, the nonlinear physics at play remain unexplored in full complexity and within a cosmological context. We present the first reproduction of the z ∼ 0 FRC using detailed synthetic observations of state-of-the-art cosmological zoom-in simulations from the Feedback in Realistic Environments (FIRE-3) suite with explicitly evolved CR proton and electron (CRe) spectra, for three models for CR transport and multichannel active galactic nucleus (AGN) feedback. In doing so, we generally verify the predictions of "calorimeter" theories at high FIR luminosities (L60 μm ≳ 109.5 L⊙) and at low FIR luminosities (L60 μm ≲ 109.5 L⊙), the so-called "conspiracy" of increasing UV radiation escape in tandem with increasing CRe escape, and find that the global FRC is insensitive to orders-of-magnitude locally variable CR transport coefficients. Importantly, the indirect effect of AGN feedback on emergent observables highlights novel interpretations of outliers in the FRC. In particular, we find that in many cases "radio-excess" objects can be better understood as "IR-dim" objects with longer-lived radio contributions at low z from Type Ia supernovae and intermittent black hole accretion in quenching galaxies, though this is sensitive to the interplay of CR transport and AGN feedback physics. This creates characteristic evolutionary tracks leading to the z = 0 FRC, which shape the subsequent late-time behavior of each model.